A = {9, -3, 5, -15, 4, 0, 7};
Position[Most@FoldList[Plus, 0, A] - Rest@Reverse@FoldList[Plus, 0, Reverse@A], 0]
{{4}, {7}}
A = Array[0 &, 10];
Position[Most@FoldList[Plus, 0, A] - Rest@Reverse@FoldList[Plus, 0, Reverse@A], 0]
{{1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}, {10}}